Properties

Label 475.2.bi.a.117.18
Level $475$
Weight $2$
Character 475.117
Analytic conductor $3.793$
Analytic rank $0$
Dimension $2304$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(2,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(180))
 
chi = DirichletCharacter(H, H._module([9, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.bi (of order \(180\), degree \(48\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(2304\)
Relative dimension: \(48\) over \(\Q(\zeta_{180})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{180}]$

Embedding invariants

Embedding label 117.18
Character \(\chi\) \(=\) 475.117
Dual form 475.2.bi.a.203.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.317394 - 0.747734i) q^{2} +(-2.54067 + 0.493857i) q^{3} +(0.930950 - 0.964027i) q^{4} +(-1.28972 - 1.82664i) q^{5} +(1.17567 + 1.74300i) q^{6} +(0.700725 - 2.61514i) q^{7} +(-2.53302 - 0.972337i) q^{8} +(3.42957 - 1.38564i) q^{9} +O(q^{10})\) \(q+(-0.317394 - 0.747734i) q^{2} +(-2.54067 + 0.493857i) q^{3} +(0.930950 - 0.964027i) q^{4} +(-1.28972 - 1.82664i) q^{5} +(1.17567 + 1.74300i) q^{6} +(0.700725 - 2.61514i) q^{7} +(-2.53302 - 0.972337i) q^{8} +(3.42957 - 1.38564i) q^{9} +(-0.956495 + 1.54413i) q^{10} +(2.63093 + 0.559221i) q^{11} +(-1.88915 + 2.90903i) q^{12} +(-2.73700 + 0.336061i) q^{13} +(-2.17784 + 0.306075i) q^{14} +(4.17885 + 4.00397i) q^{15} +(-0.0166235 - 0.476035i) q^{16} +(1.05162 - 1.75019i) q^{17} +(-2.12461 - 2.12461i) q^{18} +(-1.43935 - 4.11440i) q^{19} +(-2.96160 - 0.457192i) q^{20} +(-0.488808 + 6.99028i) q^{21} +(-0.416893 - 2.14473i) q^{22} +(-1.79825 + 5.88182i) q^{23} +(6.91578 + 1.21944i) q^{24} +(-1.67326 + 4.71171i) q^{25} +(1.11999 + 1.93988i) q^{26} +(-1.51710 + 0.985219i) q^{27} +(-1.86873 - 3.11008i) q^{28} +(-1.49369 + 5.99086i) q^{29} +(1.66756 - 4.39550i) q^{30} +(-5.90338 - 0.620470i) q^{31} +(-5.26873 + 2.45685i) q^{32} +(-6.96051 - 0.121496i) q^{33} +(-1.64245 - 0.230832i) q^{34} +(-5.68067 + 2.09282i) q^{35} +(1.85697 - 4.59616i) q^{36} +(-1.66796 - 3.27356i) q^{37} +(-2.61963 + 2.38214i) q^{38} +(6.78784 - 2.20550i) q^{39} +(1.49077 + 5.88097i) q^{40} +(-1.98844 + 0.0694379i) q^{41} +(5.38201 - 1.85318i) q^{42} +(-3.16293 - 4.51713i) q^{43} +(2.98837 - 2.01568i) q^{44} +(-6.95424 - 4.47753i) q^{45} +(4.96879 - 0.522241i) q^{46} +(-1.26579 + 0.760561i) q^{47} +(0.277328 + 1.20124i) q^{48} +(-0.285772 - 0.164991i) q^{49} +(4.05419 - 0.244318i) q^{50} +(-1.80748 + 4.96601i) q^{51} +(-2.22403 + 2.95139i) q^{52} +(0.100732 + 5.77094i) q^{53} +(1.21820 + 0.821688i) q^{54} +(-2.37166 - 5.52701i) q^{55} +(-4.31775 + 5.94288i) q^{56} +(5.68884 + 9.74251i) q^{57} +(4.95366 - 0.784583i) q^{58} +(-4.85463 + 3.03351i) q^{59} +(7.75023 - 0.301030i) q^{60} +(1.88398 - 1.00173i) q^{61} +(1.40975 + 4.61109i) q^{62} +(-1.22045 - 9.93976i) q^{63} +(2.80137 + 2.52237i) q^{64} +(4.14382 + 4.56609i) q^{65} +(2.11838 + 5.24317i) q^{66} +(3.78556 - 4.35479i) q^{67} +(-0.708224 - 2.64313i) q^{68} +(1.66400 - 15.8319i) q^{69} +(3.36788 + 3.58338i) q^{70} +(6.23890 - 3.04291i) q^{71} +(-10.0345 + 0.175153i) q^{72} +(12.6266 + 1.55036i) q^{73} +(-1.91835 + 2.28620i) q^{74} +(1.92429 - 12.7973i) q^{75} +(-5.30635 - 2.44273i) q^{76} +(3.30600 - 6.48839i) q^{77} +(-3.80355 - 4.37549i) q^{78} +(6.90926 - 10.2434i) q^{79} +(-0.848106 + 0.644315i) q^{80} +(-4.61441 + 4.45609i) q^{81} +(0.683041 + 1.46479i) q^{82} +(-3.24393 - 4.00592i) q^{83} +(6.28376 + 6.97882i) q^{84} +(-4.55326 + 0.336315i) q^{85} +(-2.37372 + 3.79874i) q^{86} +(0.836349 - 15.9585i) q^{87} +(-6.12046 - 3.97467i) q^{88} +(0.0512112 - 1.46650i) q^{89} +(-1.14076 + 6.62106i) q^{90} +(-1.03903 + 7.39312i) q^{91} +(3.99615 + 7.20924i) q^{92} +(15.3050 - 1.33901i) q^{93} +(0.970450 + 0.705073i) q^{94} +(-5.65919 + 7.93559i) q^{95} +(12.1728 - 8.84404i) q^{96} +(-8.06707 + 7.01259i) q^{97} +(-0.0326667 + 0.266049i) q^{98} +(9.79784 - 1.72762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2304 q - 48 q^{2} - 48 q^{3} - 60 q^{4} - 48 q^{5} - 36 q^{6} - 30 q^{7} - 72 q^{8} - 60 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2304 q - 48 q^{2} - 48 q^{3} - 60 q^{4} - 48 q^{5} - 36 q^{6} - 30 q^{7} - 72 q^{8} - 60 q^{9} - 48 q^{10} - 18 q^{11} - 72 q^{12} - 48 q^{13} - 60 q^{14} - 66 q^{15} - 36 q^{16} - 30 q^{17} - 60 q^{19} - 36 q^{20} - 36 q^{21} - 156 q^{22} - 120 q^{23} - 72 q^{25} - 48 q^{26} - 72 q^{27} - 60 q^{28} - 24 q^{30} - 54 q^{31} - 78 q^{32} - 90 q^{33} - 60 q^{34} - 30 q^{35} - 36 q^{36} - 204 q^{38} - 120 q^{39} + 36 q^{40} - 36 q^{41} - 84 q^{42} + 132 q^{43} - 60 q^{44} - 42 q^{45} - 54 q^{46} + 84 q^{47} - 120 q^{48} - 216 q^{50} - 96 q^{51} - 30 q^{53} - 60 q^{54} - 78 q^{55} - 234 q^{57} - 240 q^{58} + 60 q^{59} - 144 q^{60} - 36 q^{61} + 180 q^{62} + 66 q^{63} - 30 q^{64} + 288 q^{65} - 108 q^{66} - 168 q^{67} - 48 q^{68} - 90 q^{69} - 96 q^{70} - 36 q^{71} - 528 q^{72} - 66 q^{73} - 96 q^{76} - 288 q^{77} + 168 q^{78} - 60 q^{79} - 420 q^{80} - 36 q^{81} - 120 q^{82} + 90 q^{83} + 990 q^{84} + 96 q^{85} - 36 q^{86} + 216 q^{87} + 108 q^{88} - 60 q^{89} - 240 q^{90} - 36 q^{91} + 312 q^{92} + 30 q^{93} - 36 q^{95} - 72 q^{96} + 12 q^{97} - 30 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{13}{18}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.317394 0.747734i −0.224432 0.528728i 0.769510 0.638634i \(-0.220500\pi\)
−0.993942 + 0.109907i \(0.964945\pi\)
\(3\) −2.54067 + 0.493857i −1.46686 + 0.285128i −0.860250 0.509873i \(-0.829692\pi\)
−0.606608 + 0.795001i \(0.707470\pi\)
\(4\) 0.930950 0.964027i 0.465475 0.482013i
\(5\) −1.28972 1.82664i −0.576779 0.816900i
\(6\) 1.17567 + 1.74300i 0.479965 + 0.711577i
\(7\) 0.700725 2.61514i 0.264849 0.988431i −0.697493 0.716591i \(-0.745701\pi\)
0.962343 0.271839i \(-0.0876320\pi\)
\(8\) −2.53302 0.972337i −0.895559 0.343773i
\(9\) 3.42957 1.38564i 1.14319 0.461879i
\(10\) −0.956495 + 1.54413i −0.302470 + 0.488297i
\(11\) 2.63093 + 0.559221i 0.793255 + 0.168612i 0.586680 0.809819i \(-0.300435\pi\)
0.206576 + 0.978431i \(0.433768\pi\)
\(12\) −1.88915 + 2.90903i −0.545350 + 0.839765i
\(13\) −2.73700 + 0.336061i −0.759106 + 0.0932065i −0.492160 0.870505i \(-0.663792\pi\)
−0.266946 + 0.963711i \(0.586015\pi\)
\(14\) −2.17784 + 0.306075i −0.582051 + 0.0818020i
\(15\) 4.17885 + 4.00397i 1.07897 + 1.03382i
\(16\) −0.0166235 0.476035i −0.00415587 0.119009i
\(17\) 1.05162 1.75019i 0.255055 0.424483i −0.702948 0.711241i \(-0.748133\pi\)
0.958003 + 0.286758i \(0.0925777\pi\)
\(18\) −2.12461 2.12461i −0.500776 0.500776i
\(19\) −1.43935 4.11440i −0.330209 0.943908i
\(20\) −2.96160 0.457192i −0.662233 0.102231i
\(21\) −0.488808 + 6.99028i −0.106667 + 1.52540i
\(22\) −0.416893 2.14473i −0.0888819 0.457258i
\(23\) −1.79825 + 5.88182i −0.374962 + 1.22644i 0.546329 + 0.837570i \(0.316025\pi\)
−0.921291 + 0.388874i \(0.872864\pi\)
\(24\) 6.91578 + 1.21944i 1.41168 + 0.248917i
\(25\) −1.67326 + 4.71171i −0.334651 + 0.942342i
\(26\) 1.11999 + 1.93988i 0.219648 + 0.380442i
\(27\) −1.51710 + 0.985219i −0.291967 + 0.189606i
\(28\) −1.86873 3.11008i −0.353156 0.587750i
\(29\) −1.49369 + 5.99086i −0.277371 + 1.11248i 0.656345 + 0.754461i \(0.272102\pi\)
−0.933716 + 0.358015i \(0.883454\pi\)
\(30\) 1.66756 4.39550i 0.304453 0.802506i
\(31\) −5.90338 0.620470i −1.06028 0.111440i −0.441700 0.897163i \(-0.645624\pi\)
−0.618578 + 0.785723i \(0.712291\pi\)
\(32\) −5.26873 + 2.45685i −0.931388 + 0.434313i
\(33\) −6.96051 0.121496i −1.21167 0.0211498i
\(34\) −1.64245 0.230832i −0.281678 0.0395873i
\(35\) −5.68067 + 2.09282i −0.960209 + 0.353751i
\(36\) 1.85697 4.59616i 0.309495 0.766026i
\(37\) −1.66796 3.27356i −0.274211 0.538169i 0.712298 0.701877i \(-0.247655\pi\)
−0.986509 + 0.163708i \(0.947655\pi\)
\(38\) −2.61963 + 2.38214i −0.424961 + 0.386433i
\(39\) 6.78784 2.20550i 1.08692 0.353163i
\(40\) 1.49077 + 5.88097i 0.235712 + 0.929864i
\(41\) −1.98844 + 0.0694379i −0.310543 + 0.0108444i −0.189747 0.981833i \(-0.560767\pi\)
−0.120796 + 0.992677i \(0.538545\pi\)
\(42\) 5.38201 1.85318i 0.830462 0.285951i
\(43\) −3.16293 4.51713i −0.482342 0.688856i 0.502051 0.864838i \(-0.332579\pi\)
−0.984393 + 0.175982i \(0.943690\pi\)
\(44\) 2.98837 2.01568i 0.450513 0.303875i
\(45\) −6.95424 4.47753i −1.03668 0.667470i
\(46\) 4.96879 0.522241i 0.732608 0.0770002i
\(47\) −1.26579 + 0.760561i −0.184634 + 0.110939i −0.604359 0.796712i \(-0.706571\pi\)
0.419725 + 0.907651i \(0.362126\pi\)
\(48\) 0.277328 + 1.20124i 0.0400288 + 0.173384i
\(49\) −0.285772 0.164991i −0.0408246 0.0235701i
\(50\) 4.05419 0.244318i 0.573349 0.0345518i
\(51\) −1.80748 + 4.96601i −0.253098 + 0.695380i
\(52\) −2.22403 + 2.95139i −0.308418 + 0.409285i
\(53\) 0.100732 + 5.77094i 0.0138366 + 0.792699i 0.924852 + 0.380327i \(0.124189\pi\)
−0.911015 + 0.412372i \(0.864700\pi\)
\(54\) 1.21820 + 0.821688i 0.165776 + 0.111818i
\(55\) −2.37166 5.52701i −0.319794 0.745262i
\(56\) −4.31775 + 5.94288i −0.576984 + 0.794150i
\(57\) 5.68884 + 9.74251i 0.753505 + 1.29043i
\(58\) 4.95366 0.784583i 0.650448 0.103021i
\(59\) −4.85463 + 3.03351i −0.632019 + 0.394929i −0.807764 0.589506i \(-0.799322\pi\)
0.175745 + 0.984436i \(0.443767\pi\)
\(60\) 7.75023 0.301030i 1.00055 0.0388627i
\(61\) 1.88398 1.00173i 0.241219 0.128258i −0.344462 0.938800i \(-0.611938\pi\)
0.585680 + 0.810542i \(0.300827\pi\)
\(62\) 1.40975 + 4.61109i 0.179039 + 0.585609i
\(63\) −1.22045 9.93976i −0.153762 1.25229i
\(64\) 2.80137 + 2.52237i 0.350172 + 0.315296i
\(65\) 4.14382 + 4.56609i 0.513977 + 0.566354i
\(66\) 2.11838 + 5.24317i 0.260754 + 0.645390i
\(67\) 3.78556 4.35479i 0.462480 0.532022i −0.475035 0.879967i \(-0.657565\pi\)
0.937515 + 0.347945i \(0.113120\pi\)
\(68\) −0.708224 2.64313i −0.0858847 0.320526i
\(69\) 1.66400 15.8319i 0.200321 1.90593i
\(70\) 3.36788 + 3.58338i 0.402539 + 0.428296i
\(71\) 6.23890 3.04291i 0.740421 0.361127i −0.0292466 0.999572i \(-0.509311\pi\)
0.769668 + 0.638445i \(0.220422\pi\)
\(72\) −10.0345 + 0.175153i −1.18258 + 0.0206419i
\(73\) 12.6266 + 1.55036i 1.47784 + 0.181455i 0.820285 0.571955i \(-0.193815\pi\)
0.657550 + 0.753411i \(0.271593\pi\)
\(74\) −1.91835 + 2.28620i −0.223003 + 0.265765i
\(75\) 1.92429 12.7973i 0.222198 1.47770i
\(76\) −5.30635 2.44273i −0.608680 0.280200i
\(77\) 3.30600 6.48839i 0.376754 0.739421i
\(78\) −3.80355 4.37549i −0.430668 0.495426i
\(79\) 6.90926 10.2434i 0.777353 1.15247i −0.207356 0.978266i \(-0.566486\pi\)
0.984709 0.174207i \(-0.0557363\pi\)
\(80\) −0.848106 + 0.644315i −0.0948212 + 0.0720367i
\(81\) −4.61441 + 4.45609i −0.512713 + 0.495121i
\(82\) 0.683041 + 1.46479i 0.0754293 + 0.161759i
\(83\) −3.24393 4.00592i −0.356067 0.439707i 0.567366 0.823466i \(-0.307963\pi\)
−0.923433 + 0.383759i \(0.874629\pi\)
\(84\) 6.28376 + 6.97882i 0.685614 + 0.761452i
\(85\) −4.55326 + 0.336315i −0.493871 + 0.0364784i
\(86\) −2.37372 + 3.79874i −0.255964 + 0.409629i
\(87\) 0.836349 15.9585i 0.0896661 1.71093i
\(88\) −6.12046 3.97467i −0.652443 0.423701i
\(89\) 0.0512112 1.46650i 0.00542837 0.155448i −0.993650 0.112518i \(-0.964108\pi\)
0.999078 0.0429303i \(-0.0136693\pi\)
\(90\) −1.14076 + 6.62106i −0.120247 + 0.697921i
\(91\) −1.03903 + 7.39312i −0.108920 + 0.775009i
\(92\) 3.99615 + 7.20924i 0.416627 + 0.751616i
\(93\) 15.3050 1.33901i 1.58705 0.138849i
\(94\) 0.970450 + 0.705073i 0.100094 + 0.0727228i
\(95\) −5.65919 + 7.93559i −0.580621 + 0.814174i
\(96\) 12.1728 8.84404i 1.24238 0.902641i
\(97\) −8.06707 + 7.01259i −0.819086 + 0.712021i −0.960606 0.277915i \(-0.910357\pi\)
0.141519 + 0.989935i \(0.454801\pi\)
\(98\) −0.0326667 + 0.266049i −0.00329983 + 0.0268750i
\(99\) 9.79784 1.72762i 0.984720 0.173633i
\(100\) 2.98450 + 5.99943i 0.298450 + 0.599943i
\(101\) −8.92285 3.24765i −0.887857 0.323154i −0.142481 0.989798i \(-0.545508\pi\)
−0.745376 + 0.666644i \(0.767730\pi\)
\(102\) 4.28693 0.224669i 0.424470 0.0222455i
\(103\) 11.2503 13.8929i 1.10852 1.36891i 0.186186 0.982514i \(-0.440387\pi\)
0.922334 0.386394i \(-0.126279\pi\)
\(104\) 7.25964 + 1.81003i 0.711866 + 0.177488i
\(105\) 13.3992 8.12260i 1.30763 0.792685i
\(106\) 4.28316 1.90698i 0.416017 0.185223i
\(107\) −14.4969 3.88445i −1.40147 0.375524i −0.522599 0.852578i \(-0.675038\pi\)
−0.878874 + 0.477055i \(0.841704\pi\)
\(108\) −0.462571 + 2.37972i −0.0445109 + 0.228989i
\(109\) −1.21833 0.647797i −0.116695 0.0620477i 0.410098 0.912041i \(-0.365494\pi\)
−0.526793 + 0.849994i \(0.676606\pi\)
\(110\) −3.37998 + 3.52761i −0.322269 + 0.336344i
\(111\) 5.85441 + 7.49330i 0.555676 + 0.711233i
\(112\) −1.25655 0.290097i −0.118732 0.0274116i
\(113\) 13.5508 6.90450i 1.27476 0.649521i 0.320143 0.947369i \(-0.396269\pi\)
0.954613 + 0.297848i \(0.0962689\pi\)
\(114\) 5.47920 7.34595i 0.513174 0.688011i
\(115\) 13.0632 4.30112i 1.21815 0.401081i
\(116\) 4.38480 + 7.01715i 0.407119 + 0.651526i
\(117\) −8.92106 + 4.94503i −0.824753 + 0.457168i
\(118\) 3.80909 + 2.66715i 0.350655 + 0.245531i
\(119\) −3.84009 3.97653i −0.352021 0.364528i
\(120\) −6.69192 14.2054i −0.610886 1.29677i
\(121\) −3.43994 1.53156i −0.312721 0.139233i
\(122\) −1.34699 1.09077i −0.121951 0.0987539i
\(123\) 5.01769 1.15842i 0.452430 0.104452i
\(124\) −6.09390 + 5.11339i −0.547248 + 0.459196i
\(125\) 10.7646 3.02033i 0.962819 0.270146i
\(126\) −7.04494 + 4.06740i −0.627613 + 0.362352i
\(127\) −8.01861 8.59891i −0.711537 0.763030i 0.268190 0.963366i \(-0.413574\pi\)
−0.979727 + 0.200336i \(0.935797\pi\)
\(128\) −2.78839 + 8.09808i −0.246461 + 0.715776i
\(129\) 10.2668 + 9.91451i 0.903940 + 0.872924i
\(130\) 2.09900 4.54772i 0.184094 0.398862i
\(131\) −4.41376 17.7026i −0.385632 1.54669i −0.778832 0.627233i \(-0.784188\pi\)
0.393200 0.919453i \(-0.371368\pi\)
\(132\) −6.59701 + 6.59701i −0.574196 + 0.574196i
\(133\) −11.7683 + 0.881038i −1.02044 + 0.0763957i
\(134\) −4.45774 1.44841i −0.385090 0.125123i
\(135\) 3.75628 + 1.50056i 0.323289 + 0.129147i
\(136\) −4.36555 + 3.41074i −0.374343 + 0.292469i
\(137\) 9.81782 + 13.0287i 0.838793 + 1.11312i 0.992163 + 0.124947i \(0.0398760\pi\)
−0.153371 + 0.988169i \(0.549013\pi\)
\(138\) −12.3662 + 3.78071i −1.05268 + 0.321836i
\(139\) −9.06844 0.316677i −0.769175 0.0268602i −0.352376 0.935859i \(-0.614626\pi\)
−0.416800 + 0.908998i \(0.636848\pi\)
\(140\) −3.27089 + 7.42463i −0.276440 + 0.627496i
\(141\) 2.84034 2.55745i 0.239200 0.215376i
\(142\) −4.25548 3.69923i −0.357112 0.310433i
\(143\) −7.38878 0.646434i −0.617881 0.0540575i
\(144\) −0.716623 1.60956i −0.0597185 0.134130i
\(145\) 12.8696 4.99808i 1.06876 0.415068i
\(146\) −2.84837 9.93343i −0.235732 0.822097i
\(147\) 0.807535 + 0.278057i 0.0666044 + 0.0229337i
\(148\) −4.70858 1.43956i −0.387043 0.118331i
\(149\) −0.951353 2.61382i −0.0779379 0.214133i 0.894604 0.446859i \(-0.147457\pi\)
−0.972542 + 0.232727i \(0.925235\pi\)
\(150\) −10.1797 + 2.62292i −0.831169 + 0.214161i
\(151\) 9.61288i 0.782285i 0.920330 + 0.391143i \(0.127920\pi\)
−0.920330 + 0.391143i \(0.872080\pi\)
\(152\) −0.354677 + 11.8214i −0.0287681 + 0.958842i
\(153\) 1.18148 7.45956i 0.0955168 0.603070i
\(154\) −5.90090 0.412631i −0.475508 0.0332508i
\(155\) 6.48031 + 11.5836i 0.520511 + 0.930417i
\(156\) 4.19298 8.59688i 0.335707 0.688301i
\(157\) −8.75827 + 6.13261i −0.698986 + 0.489436i −0.868245 0.496136i \(-0.834752\pi\)
0.169258 + 0.985572i \(0.445863\pi\)
\(158\) −9.85230 1.91509i −0.783807 0.152357i
\(159\) −3.10594 14.6123i −0.246317 1.15883i
\(160\) 11.2830 + 6.45545i 0.891996 + 0.510348i
\(161\) 14.1217 + 8.82422i 1.11295 + 0.695446i
\(162\) 4.79656 + 2.03602i 0.376853 + 0.159965i
\(163\) −22.5381 1.18117i −1.76532 0.0925167i −0.858183 0.513345i \(-0.828406\pi\)
−0.907140 + 0.420828i \(0.861740\pi\)
\(164\) −1.78420 + 1.98156i −0.139323 + 0.154733i
\(165\) 8.75516 + 12.8711i 0.681588 + 1.00201i
\(166\) −1.96576 + 3.69705i −0.152572 + 0.286947i
\(167\) −0.972693 2.82491i −0.0752693 0.218598i 0.901545 0.432685i \(-0.142434\pi\)
−0.976815 + 0.214087i \(0.931322\pi\)
\(168\) 8.03507 17.2313i 0.619919 1.32942i
\(169\) −5.23564 + 1.30539i −0.402741 + 0.100415i
\(170\) 1.69665 + 3.29789i 0.130127 + 0.252936i
\(171\) −10.6374 12.1162i −0.813463 0.926550i
\(172\) −7.29916 1.15607i −0.556556 0.0881498i
\(173\) −0.0379277 + 0.0160993i −0.00288359 + 0.00122401i −0.392172 0.919892i \(-0.628276\pi\)
0.389289 + 0.921116i \(0.372721\pi\)
\(174\) −12.1982 + 4.43977i −0.924740 + 0.336578i
\(175\) 11.1493 + 7.67742i 0.842808 + 0.580358i
\(176\) 0.222474 1.26171i 0.0167696 0.0951050i
\(177\) 10.8359 10.1046i 0.814477 0.759512i
\(178\) −1.11280 + 0.427165i −0.0834081 + 0.0320174i
\(179\) −1.78240 16.9584i −0.133223 1.26753i −0.833041 0.553211i \(-0.813402\pi\)
0.699818 0.714321i \(-0.253264\pi\)
\(180\) −10.7905 + 2.53572i −0.804277 + 0.189002i
\(181\) −0.772737 11.0507i −0.0574371 0.821388i −0.937819 0.347124i \(-0.887158\pi\)
0.880382 0.474265i \(-0.157286\pi\)
\(182\) 5.85787 1.56961i 0.434214 0.116347i
\(183\) −4.29186 + 3.47548i −0.317264 + 0.256915i
\(184\) 10.2741 13.1503i 0.757419 0.969452i
\(185\) −3.82843 + 7.26873i −0.281471 + 0.534408i
\(186\) −5.85893 11.0191i −0.429598 0.807956i
\(187\) 3.74548 4.01654i 0.273897 0.293718i
\(188\) −0.445182 + 1.92829i −0.0324682 + 0.140635i
\(189\) 1.51341 + 4.65781i 0.110085 + 0.338806i
\(190\) 7.72990 + 1.71286i 0.560786 + 0.124264i
\(191\) −3.86160 + 11.8848i −0.279416 + 0.859953i 0.708602 + 0.705609i \(0.249326\pi\)
−0.988017 + 0.154344i \(0.950674\pi\)
\(192\) −8.36306 5.02504i −0.603552 0.362651i
\(193\) 16.4472 + 7.66944i 1.18389 + 0.552058i 0.911968 0.410261i \(-0.134562\pi\)
0.271924 + 0.962319i \(0.412340\pi\)
\(194\) 7.80399 + 3.80626i 0.560294 + 0.273274i
\(195\) −12.7831 9.55450i −0.915415 0.684212i
\(196\) −0.425095 + 0.121894i −0.0303639 + 0.00870672i
\(197\) 3.49659 + 9.10894i 0.249122 + 0.648985i 0.999934 0.0115315i \(-0.00367066\pi\)
−0.750811 + 0.660517i \(0.770337\pi\)
\(198\) −4.40158 6.77784i −0.312807 0.481680i
\(199\) −17.3186 20.6395i −1.22768 1.46310i −0.841132 0.540831i \(-0.818110\pi\)
−0.386553 0.922267i \(-0.626334\pi\)
\(200\) 8.81977 10.3079i 0.623652 0.728879i
\(201\) −7.46723 + 12.9336i −0.526698 + 0.912267i
\(202\) 0.403682 + 7.70271i 0.0284029 + 0.541960i
\(203\) 14.6203 + 8.10416i 1.02614 + 0.568801i
\(204\) 3.10469 + 6.36556i 0.217372 + 0.445678i
\(205\) 2.69137 + 3.54262i 0.187973 + 0.247427i
\(206\) −13.9590 4.00267i −0.972567 0.278879i
\(207\) 1.98283 + 22.6638i 0.137816 + 1.57525i
\(208\) 0.205475 + 1.29732i 0.0142471 + 0.0899528i
\(209\) −1.48597 11.6296i −0.102786 0.804437i
\(210\) −10.3264 7.44095i −0.712587 0.513474i
\(211\) 22.2164 + 8.97599i 1.52944 + 0.617933i 0.976544 0.215319i \(-0.0690791\pi\)
0.552894 + 0.833252i \(0.313524\pi\)
\(212\) 5.65712 + 5.27535i 0.388532 + 0.362312i
\(213\) −14.3482 + 10.8122i −0.983125 + 0.740838i
\(214\) 1.69672 + 12.0728i 0.115985 + 0.825277i
\(215\) −4.17190 + 11.6034i −0.284522 + 0.791343i
\(216\) 4.80083 1.02045i 0.326655 0.0694327i
\(217\) −5.75926 + 15.0034i −0.390964 + 1.01850i
\(218\) −0.0976892 + 1.11659i −0.00661635 + 0.0756252i
\(219\) −32.8458 + 2.29680i −2.21951 + 0.155203i
\(220\) −7.53608 2.85903i −0.508082 0.192756i
\(221\) −2.29011 + 5.14367i −0.154049 + 0.346000i
\(222\) 3.74484 6.75587i 0.251337 0.453424i
\(223\) 21.4726 + 16.1808i 1.43791 + 1.08354i 0.980995 + 0.194035i \(0.0621575\pi\)
0.456917 + 0.889509i \(0.348954\pi\)
\(224\) 2.73307 + 15.5000i 0.182611 + 1.03564i
\(225\) 0.790163 + 18.4777i 0.0526775 + 1.23184i
\(226\) −9.46369 7.94098i −0.629515 0.528226i
\(227\) −7.33853 3.73917i −0.487075 0.248177i 0.193165 0.981166i \(-0.438125\pi\)
−0.680241 + 0.732989i \(0.738125\pi\)
\(228\) 14.6881 + 3.58560i 0.972740 + 0.237462i
\(229\) 9.43080 + 12.9804i 0.623205 + 0.857767i 0.997581 0.0695092i \(-0.0221433\pi\)
−0.374377 + 0.927277i \(0.622143\pi\)
\(230\) −7.36229 8.40267i −0.485455 0.554056i
\(231\) −5.19513 + 18.1176i −0.341815 + 1.19205i
\(232\) 9.60869 13.7226i 0.630842 0.900935i
\(233\) 0.342508 19.6223i 0.0224385 1.28550i −0.754658 0.656118i \(-0.772197\pi\)
0.777097 0.629381i \(-0.216692\pi\)
\(234\) 6.52906 + 5.10106i 0.426818 + 0.333467i
\(235\) 3.02178 + 1.33123i 0.197119 + 0.0868400i
\(236\) −1.59503 + 7.50404i −0.103828 + 0.488471i
\(237\) −12.4954 + 29.4373i −0.811663 + 1.91216i
\(238\) −1.75457 + 4.13350i −0.113732 + 0.267935i
\(239\) 4.25462 20.0164i 0.275209 1.29475i −0.595659 0.803237i \(-0.703109\pi\)
0.870868 0.491518i \(-0.163558\pi\)
\(240\) 1.83656 2.05584i 0.118549 0.132704i
\(241\) −11.4780 8.96756i −0.739360 0.577651i 0.174028 0.984741i \(-0.444322\pi\)
−0.913388 + 0.407089i \(0.866544\pi\)
\(242\) −0.0533822 + 3.05826i −0.00343154 + 0.196593i
\(243\) 12.6357 18.0457i 0.810583 1.15763i
\(244\) 0.788196 2.74877i 0.0504591 0.175972i
\(245\) 0.0671862 + 0.734795i 0.00429237 + 0.0469444i
\(246\) −2.45878 3.38422i −0.156766 0.215770i
\(247\) 5.32218 + 10.7774i 0.338642 + 0.685748i
\(248\) 14.3501 + 7.31174i 0.911232 + 0.464296i
\(249\) 10.2201 + 8.57569i 0.647673 + 0.543462i
\(250\) −5.67504 7.09046i −0.358921 0.448440i
\(251\) 0.140790 + 0.798463i 0.00888662 + 0.0503985i 0.988929 0.148392i \(-0.0474098\pi\)
−0.980042 + 0.198791i \(0.936299\pi\)
\(252\) −10.7184 8.07688i −0.675194 0.508795i
\(253\) −8.02032 + 14.4690i −0.504233 + 0.909660i
\(254\) −3.88464 + 8.72503i −0.243744 + 0.547457i
\(255\) 11.4023 3.10312i 0.714037 0.194325i
\(256\) 14.4611 1.01122i 0.903819 0.0632012i
\(257\) 2.33443 26.6827i 0.145618 1.66442i −0.474758 0.880116i \(-0.657464\pi\)
0.620376 0.784305i \(-0.286980\pi\)
\(258\) 4.15480 10.8236i 0.258667 0.673850i
\(259\) −9.72960 + 2.06809i −0.604568 + 0.128505i
\(260\) 8.25952 + 0.256055i 0.512234 + 0.0158799i
\(261\) 3.17844 + 22.6158i 0.196741 + 1.39988i
\(262\) −11.8360 + 8.91903i −0.731228 + 0.551019i
\(263\) 13.2773 + 12.3813i 0.818713 + 0.763462i 0.974514 0.224326i \(-0.0720181\pi\)
−0.155801 + 0.987788i \(0.549796\pi\)
\(264\) 17.5130 + 7.07571i 1.07785 + 0.435480i
\(265\) 10.4115 7.62688i 0.639576 0.468516i
\(266\) 4.39398 + 8.51994i 0.269412 + 0.522391i
\(267\) 0.594128 + 3.75118i 0.0363600 + 0.229568i
\(268\) −0.673967 7.70347i −0.0411691 0.470564i
\(269\) −24.3537 6.98331i −1.48487 0.425780i −0.567354 0.823474i \(-0.692033\pi\)
−0.917518 + 0.397694i \(0.869811\pi\)
\(270\) −0.0702057 3.28497i −0.00427258 0.199917i
\(271\) −3.78940 7.76943i −0.230190 0.471959i 0.752168 0.658972i \(-0.229008\pi\)
−0.982358 + 0.187013i \(0.940119\pi\)
\(272\) −0.850632 0.471513i −0.0515771 0.0285897i
\(273\) −1.01129 19.2966i −0.0612063 1.16788i
\(274\) 6.62587 11.4763i 0.400283 0.693311i
\(275\) −7.03711 + 11.4605i −0.424354 + 0.691092i
\(276\) −13.7132 16.3428i −0.825440 0.983721i
\(277\) −10.4299 16.0607i −0.626672 0.964991i −0.999315 0.0370159i \(-0.988215\pi\)
0.372642 0.927975i \(-0.378452\pi\)
\(278\) 2.64148 + 6.88130i 0.158426 + 0.412713i
\(279\) −21.1058 + 6.05199i −1.26357 + 0.362323i
\(280\) 16.4242 + 0.222365i 0.981534 + 0.0132889i
\(281\) 8.42442 + 4.10886i 0.502559 + 0.245114i 0.672170 0.740397i \(-0.265362\pi\)
−0.169611 + 0.985511i \(0.554251\pi\)
\(282\) −2.81380 1.31210i −0.167559 0.0781342i
\(283\) −12.4361 7.47235i −0.739248 0.444185i 0.0950686 0.995471i \(-0.469693\pi\)
−0.834316 + 0.551286i \(0.814137\pi\)
\(284\) 2.87465 8.84727i 0.170579 0.524989i
\(285\) 10.4591 22.9566i 0.619544 1.35983i
\(286\) 1.86179 + 5.73001i 0.110090 + 0.338823i
\(287\) −1.21176 + 5.24872i −0.0715280 + 0.309822i
\(288\) −14.6652 + 15.7265i −0.864153 + 0.926691i
\(289\) 6.02376 + 11.3290i 0.354339 + 0.666414i
\(290\) −7.82198 8.03669i −0.459322 0.471930i
\(291\) 17.0326 21.8007i 0.998466 1.27798i
\(292\) 13.2493 10.7291i 0.775359 0.627873i
\(293\) −17.9922 + 4.82099i −1.05111 + 0.281645i −0.742712 0.669611i \(-0.766461\pi\)
−0.308402 + 0.951256i \(0.599794\pi\)
\(294\) −0.0483946 0.692075i −0.00282243 0.0403626i
\(295\) 11.8022 + 4.95531i 0.687153 + 0.288509i
\(296\) 1.04198 + 9.91382i 0.0605641 + 0.576229i
\(297\) −4.54235 + 1.74365i −0.263574 + 0.101177i
\(298\) −1.65249 + 1.54097i −0.0957261 + 0.0892660i
\(299\) 2.94516 16.7028i 0.170323 0.965950i
\(300\) −10.5455 13.7687i −0.608844 0.794935i
\(301\) −14.0293 + 5.10624i −0.808634 + 0.294319i
\(302\) 7.18788 3.05107i 0.413616 0.175570i
\(303\) 24.2739 + 3.84461i 1.39450 + 0.220867i
\(304\) −1.93467 + 0.753575i −0.110961 + 0.0432205i
\(305\) −4.25961 2.14941i −0.243904 0.123075i
\(306\) −5.95276 + 1.48419i −0.340297 + 0.0848455i
\(307\) 13.0151 27.9110i 0.742812 1.59297i −0.0610384 0.998135i \(-0.519441\pi\)
0.803851 0.594831i \(-0.202781\pi\)
\(308\) −3.17726 9.22744i −0.181041 0.525782i
\(309\) −21.7221 + 40.8533i −1.23573 + 2.32406i
\(310\) 6.60464 8.52212i 0.375118 0.484024i
\(311\) −19.0696 + 21.1789i −1.08134 + 1.20095i −0.102837 + 0.994698i \(0.532792\pi\)
−0.978500 + 0.206248i \(0.933875\pi\)
\(312\) −19.3383 1.01348i −1.09481 0.0573768i
\(313\) −5.77807 2.45264i −0.326596 0.138632i 0.221236 0.975220i \(-0.428991\pi\)
−0.547831 + 0.836589i \(0.684547\pi\)
\(314\) 7.36539 + 4.60240i 0.415653 + 0.259729i
\(315\) −16.5824 + 15.0488i −0.934311 + 0.847905i
\(316\) −3.44274 16.1968i −0.193669 0.911142i
\(317\) −2.13496 0.414994i −0.119911 0.0233084i 0.130497 0.991449i \(-0.458343\pi\)
−0.250408 + 0.968140i \(0.580565\pi\)
\(318\) −9.94032 + 6.96029i −0.557425 + 0.390313i
\(319\) −7.28001 + 14.9262i −0.407603 + 0.835709i
\(320\) 0.994488 8.37026i 0.0555936 0.467912i
\(321\) 38.7504 + 2.70969i 2.16283 + 0.151240i
\(322\) 2.11602 13.3600i 0.117921 0.744526i
\(323\) −8.71462 1.80765i −0.484894 0.100580i
\(324\) 8.59681i 0.477601i
\(325\) 2.99628 13.4582i 0.166204 0.746529i
\(326\) 6.27027 + 17.2274i 0.347278 + 0.954139i
\(327\) 3.41529 + 1.04416i 0.188866 + 0.0577422i
\(328\) 5.10429 + 1.75755i 0.281837 + 0.0970444i
\(329\) 1.10201 + 3.84315i 0.0607556 + 0.211880i
\(330\) 6.84530 10.6317i 0.376821 0.585257i
\(331\) −0.605736 1.36050i −0.0332942 0.0747801i 0.896133 0.443786i \(-0.146365\pi\)
−0.929427 + 0.369006i \(0.879698\pi\)
\(332\) −6.88175 0.602075i −0.377685 0.0330431i
\(333\) −10.2563 8.91571i −0.562044 0.488578i
\(334\) −1.80355 + 1.62392i −0.0986859 + 0.0888572i
\(335\) −12.8370 1.29842i −0.701358 0.0709405i
\(336\) 3.33574 + 0.116487i 0.181980 + 0.00635486i
\(337\) 20.6010 6.29836i 1.12221 0.343094i 0.324349 0.945937i \(-0.394855\pi\)
0.797859 + 0.602844i \(0.205966\pi\)
\(338\) 2.63785 + 3.50054i 0.143480 + 0.190404i
\(339\) −31.0184 + 24.2343i −1.68469 + 1.31622i
\(340\) −3.91464 + 4.70256i −0.212301 + 0.255032i
\(341\) −15.1844 4.93371i −0.822281 0.267175i
\(342\) −5.68345 + 11.7996i −0.307326 + 0.638047i
\(343\) 12.7692 12.7692i 0.689472 0.689472i
\(344\) 3.61960 + 14.5174i 0.195156 + 0.782727i
\(345\) −31.0653 + 17.3791i −1.67250 + 0.935659i
\(346\) 0.0240760 + 0.0232500i 0.00129434 + 0.00124993i
\(347\) 3.96926 11.5276i 0.213081 0.618833i −0.786917 0.617059i \(-0.788324\pi\)
0.999998 0.00177416i \(-0.000564732\pi\)
\(348\) −14.6058 15.6628i −0.782954 0.839615i
\(349\) 17.2582 9.96401i 0.923808 0.533361i 0.0389603 0.999241i \(-0.487595\pi\)
0.884848 + 0.465880i \(0.154262\pi\)
\(350\) 2.20194 10.7735i 0.117699 0.575866i
\(351\) 3.82122 3.20638i 0.203961 0.171144i
\(352\) −15.2356 + 3.51741i −0.812059 + 0.187478i
\(353\) −8.58260 6.95006i −0.456806 0.369914i 0.373124 0.927781i \(-0.378287\pi\)
−0.829930 + 0.557867i \(0.811620\pi\)
\(354\) −10.9948 4.89522i −0.584369 0.260178i
\(355\) −13.6047 7.47175i −0.722065 0.396559i
\(356\) −1.36607 1.41460i −0.0724014 0.0749738i
\(357\) 11.7203 + 8.20662i 0.620302 + 0.434340i
\(358\) −12.1147 + 6.71527i −0.640280 + 0.354913i
\(359\) −12.0350 19.2600i −0.635181 1.01650i −0.996462 0.0840445i \(-0.973216\pi\)
0.361281 0.932457i \(-0.382339\pi\)
\(360\) 13.2616 + 18.1035i 0.698948 + 0.954141i
\(361\) −14.8566 + 11.8441i −0.781924 + 0.623374i
\(362\) −8.01768 + 4.08521i −0.421400 + 0.214714i
\(363\) 9.49612 + 2.19235i 0.498417 + 0.115069i
\(364\) 6.15987 + 7.88428i 0.322865 + 0.413249i
\(365\) −13.4528 25.0639i −0.704154 1.31190i
\(366\) 3.96095 + 2.10607i 0.207042 + 0.110086i
\(367\) 3.07792 15.8345i 0.160666 0.826555i −0.810057 0.586352i \(-0.800564\pi\)
0.970723 0.240203i \(-0.0772141\pi\)
\(368\) 2.82984 + 0.758254i 0.147516 + 0.0395267i
\(369\) −6.72329 + 2.99340i −0.350000 + 0.155830i
\(370\) 6.65020 + 0.555589i 0.345727 + 0.0288837i
\(371\) 15.1624 + 3.78041i 0.787193 + 0.196269i
\(372\) 12.9573 16.0010i 0.671806 0.829611i
\(373\) −16.7024 + 0.875336i −0.864817 + 0.0453232i −0.479584 0.877496i \(-0.659212\pi\)
−0.385233 + 0.922819i \(0.625879\pi\)
\(374\) −4.19209 1.52580i −0.216768 0.0788971i
\(375\) −25.8578 + 12.9899i −1.33529 + 0.670794i
\(376\) 3.94579 0.695749i 0.203488 0.0358805i
\(377\) 2.07493 16.8989i 0.106864 0.870340i
\(378\) 3.00245 2.60999i 0.154430 0.134244i
\(379\) 18.0745 13.1319i 0.928426 0.674541i −0.0171811 0.999852i \(-0.505469\pi\)
0.945607 + 0.325312i \(0.105469\pi\)
\(380\) 2.38170 + 12.8432i 0.122179 + 0.658845i
\(381\) 24.6193 + 17.8870i 1.26129 + 0.916377i
\(382\) 10.1123 0.884712i 0.517391 0.0452658i
\(383\) 13.6270 + 24.5838i 0.696307 + 1.25617i 0.956814 + 0.290700i \(0.0938880\pi\)
−0.260507 + 0.965472i \(0.583890\pi\)
\(384\) 3.08510 21.9516i 0.157436 1.12021i
\(385\) −16.1158 + 2.32931i −0.821337 + 0.118712i
\(386\) 0.514464 14.7323i 0.0261856 0.749856i
\(387\) −17.1066 11.1091i −0.869577 0.564710i
\(388\) −0.749706 + 14.3052i −0.0380605 + 0.726238i
\(389\) −8.40271 + 13.4471i −0.426034 + 0.681797i −0.989531 0.144321i \(-0.953900\pi\)
0.563497 + 0.826118i \(0.309456\pi\)
\(390\) −3.08695 + 12.5909i −0.156314 + 0.637564i
\(391\) 8.40322 + 9.33272i 0.424969 + 0.471976i
\(392\) 0.563441 + 0.695792i 0.0284581 + 0.0351428i
\(393\) 19.9565 + 42.7968i 1.00667 + 2.15881i
\(394\) 5.70126 5.50565i 0.287226 0.277370i
\(395\) −27.6220 + 0.590333i −1.38982 + 0.0297029i
\(396\) 7.45582 11.0537i 0.374669 0.555470i
\(397\) 5.59522 + 6.43656i 0.280816 + 0.323042i 0.877631 0.479337i \(-0.159123\pi\)
−0.596815 + 0.802379i \(0.703567\pi\)
\(398\) −9.93605 + 19.5006i −0.498049 + 0.977476i
\(399\) 29.4643 8.05029i 1.47506 0.403019i
\(400\) 2.27075 + 0.718203i 0.113538 + 0.0359102i
\(401\) 16.2799 19.4017i 0.812981 0.968874i −0.186927 0.982374i \(-0.559853\pi\)
0.999909 + 0.0135002i \(0.00429737\pi\)
\(402\) 12.0410 + 1.47844i 0.600549 + 0.0737381i
\(403\) 16.3660 0.285670i 0.815250 0.0142302i
\(404\) −11.4376 + 5.57847i −0.569039 + 0.277539i
\(405\) 14.0910 + 2.68180i 0.700186 + 0.133260i
\(406\) 1.41936 13.5043i 0.0704416 0.670207i
\(407\) −2.55764 9.54526i −0.126778 0.473141i
\(408\) 9.40702 10.8215i 0.465717 0.535746i
\(409\) 6.30481 + 15.6050i 0.311753 + 0.771616i 0.998979 + 0.0451722i \(0.0143836\pi\)
−0.687226 + 0.726443i \(0.741172\pi\)
\(410\) 1.79471 3.13683i 0.0886346 0.154917i
\(411\) −31.3782 28.2530i −1.54777 1.39362i
\(412\) −2.91971 23.7791i −0.143844 1.17151i
\(413\) 4.53130 + 14.8212i 0.222971 + 0.729304i
\(414\) 16.3172 8.67600i 0.801946 0.426402i
\(415\) −3.13363 + 11.0920i −0.153824 + 0.544485i
\(416\) 13.5948 8.49499i 0.666541 0.416501i
\(417\) 23.1963 3.67394i 1.13593 0.179914i
\(418\) −8.22422 + 4.80228i −0.402260 + 0.234887i
\(419\) −14.2677 + 19.6377i −0.697020 + 0.959366i 0.302959 + 0.953003i \(0.402025\pi\)
−0.999980 + 0.00636277i \(0.997975\pi\)
\(420\) 4.64355 20.4789i 0.226582 0.999268i
\(421\) −0.832551 0.561563i −0.0405761 0.0273689i 0.538737 0.842474i \(-0.318902\pi\)
−0.579313 + 0.815105i \(0.696679\pi\)
\(422\) −0.339691 19.4609i −0.0165359 0.947340i
\(423\) −3.28724 + 4.36232i −0.159831 + 0.212103i
\(424\) 5.35614 14.7159i 0.260117 0.714666i
\(425\) 6.48675 + 7.88344i 0.314654 + 0.382403i
\(426\) 12.6387 + 7.29694i 0.612346 + 0.353538i
\(427\) −1.29951 5.62881i −0.0628879 0.272397i
\(428\) −17.2406 + 10.3592i −0.833358 + 0.500732i
\(429\) 19.0917 2.00662i 0.921756 0.0968805i
\(430\) 10.0004 0.563367i 0.482261 0.0271680i
\(431\) −30.7647 + 20.7511i −1.48188 + 0.999543i −0.490093 + 0.871670i \(0.663037\pi\)
−0.991791 + 0.127873i \(0.959185\pi\)
\(432\) 0.494218 + 0.705817i 0.0237781 + 0.0339586i
\(433\) 9.72472 3.34849i 0.467340 0.160918i −0.0817994 0.996649i \(-0.526067\pi\)
0.549139 + 0.835731i \(0.314956\pi\)
\(434\) 13.0465 0.455594i 0.626252 0.0218692i
\(435\) −30.2291 + 19.0542i −1.44938 + 0.913581i
\(436\) −1.75870 + 0.571435i −0.0842263 + 0.0273668i
\(437\) 26.7885 1.06726i 1.28147 0.0510539i
\(438\) 12.1425 + 23.8309i 0.580189 + 1.13869i
\(439\) −11.2112 + 27.7487i −0.535081 + 1.32437i 0.381443 + 0.924393i \(0.375427\pi\)
−0.916524 + 0.399980i \(0.869017\pi\)
\(440\) 0.633351 + 16.3061i 0.0301938 + 0.777363i
\(441\) −1.20869 0.169871i −0.0575568 0.00808908i
\(442\) 4.57296 + 0.0798213i 0.217514 + 0.00379671i
\(443\) 28.6934 13.3799i 1.36326 0.635700i 0.403105 0.915154i \(-0.367931\pi\)
0.960159 + 0.279453i \(0.0901532\pi\)
\(444\) 12.6739 + 1.33208i 0.601477 + 0.0632178i
\(445\) −2.74481 + 1.79782i −0.130117 + 0.0852249i
\(446\) 5.28363 21.1915i 0.250187 1.00345i
\(447\) 3.70793 + 6.17103i 0.175379 + 0.291880i
\(448\) 8.55934 5.55850i 0.404391 0.262615i
\(449\) −10.0635 17.4304i −0.474924 0.822592i 0.524664 0.851309i \(-0.324191\pi\)
−0.999588 + 0.0287175i \(0.990858\pi\)
\(450\) 13.5656 6.45554i 0.639488 0.304317i
\(451\) −5.27028 0.929293i −0.248168 0.0437587i
\(452\) 5.95904 19.4911i 0.280289 0.916785i
\(453\) −4.74739 24.4232i −0.223052 1.14750i
\(454\) −0.466696 + 6.67406i −0.0219031 + 0.313229i
\(455\) 14.8447 7.63709i 0.695928 0.358032i
\(456\) −4.93696 30.2095i −0.231194 1.41469i
\(457\) −8.83834 8.83834i −0.413440 0.413440i 0.469495 0.882935i \(-0.344436\pi\)
−0.882935 + 0.469495i \(0.844436\pi\)
\(458\) 6.71259 11.1716i 0.313659 0.522016i
\(459\) 0.128903 + 3.69130i 0.00601667 + 0.172295i
\(460\) 8.01482 16.5974i 0.373693 0.773859i
\(461\) 41.1702 5.78610i 1.91749 0.269485i 0.923908 0.382614i \(-0.124976\pi\)
0.993580 + 0.113129i \(0.0360872\pi\)
\(462\) 15.1960 1.86584i 0.706983 0.0868066i
\(463\) −9.21654 + 14.1922i −0.428329 + 0.659569i −0.985274 0.170980i \(-0.945307\pi\)
0.556945 + 0.830549i \(0.311973\pi\)
\(464\) 2.87669 + 0.611459i 0.133547 + 0.0283863i
\(465\) −22.1850 26.2298i −1.02880 1.21638i
\(466\) −14.7810 + 5.97190i −0.684715 + 0.276643i
\(467\) 38.3664 + 14.7275i 1.77539 + 0.681507i 0.998664 + 0.0516650i \(0.0164528\pi\)
0.776723 + 0.629842i \(0.216881\pi\)
\(468\) −3.53792 + 13.2037i −0.163541 + 0.610342i
\(469\) −8.73575 12.9513i −0.403380 0.598035i
\(470\) 0.0363114 2.68201i 0.00167492 0.123712i
\(471\) 19.2233 19.9063i 0.885762 0.917233i
\(472\) 15.2465 2.96362i 0.701777 0.136412i
\(473\) −5.79537 13.6530i −0.266471 0.627767i
\(474\) 25.9772 1.19317
\(475\) 21.7943 + 0.102655i 0.999989 + 0.00471015i
\(476\) −7.40842 −0.339564
\(477\) 8.34189 + 19.6523i 0.381949 + 0.899815i
\(478\) −16.3174 + 3.17177i −0.746338 + 0.145073i
\(479\) 19.3937 20.0828i 0.886121 0.917605i −0.110970 0.993824i \(-0.535396\pi\)
0.997091 + 0.0762188i \(0.0242847\pi\)
\(480\) −31.8544 10.8290i −1.45395 0.494275i
\(481\) 5.66532 + 8.39918i 0.258316 + 0.382969i
\(482\) −3.06231 + 11.4287i −0.139485 + 0.520563i
\(483\) −40.2365 15.4454i −1.83083 0.702788i
\(484\) −4.67887 + 1.89039i −0.212676 + 0.0859267i
\(485\) 23.2137 + 5.69139i 1.05408 + 0.258433i
\(486\) −17.5039 3.72057i −0.793993 0.168768i
\(487\) 11.2244 17.2840i 0.508625 0.783213i −0.487316 0.873226i \(-0.662024\pi\)
0.995941 + 0.0900123i \(0.0286907\pi\)
\(488\) −5.74619 + 0.705543i −0.260118 + 0.0319384i
\(489\) 57.8454 8.12963i 2.61586 0.367635i
\(490\) 0.528107 0.283457i 0.0238574 0.0128053i
\(491\) −0.0638065 1.82718i −0.00287955 0.0824594i −0.999980 0.00635991i \(-0.997976\pi\)
0.997100 0.0760995i \(-0.0242467\pi\)
\(492\) 3.55446 5.91562i 0.160248 0.266697i
\(493\) 8.91435 + 8.91435i 0.401482 + 0.401482i
\(494\) 6.36939 7.40025i 0.286572 0.332953i
\(495\) −15.7922 15.6690i −0.709806 0.704270i
\(496\) −0.197230 + 2.82053i −0.00885591 + 0.126645i
\(497\) −3.58590 18.4478i −0.160850 0.827499i
\(498\) 3.16853 10.3638i 0.141985 0.464413i
\(499\) 36.8085 + 6.49034i 1.64778 + 0.290547i 0.919016 0.394221i \(-0.128985\pi\)
0.728761 + 0.684768i \(0.240097\pi\)
\(500\) 7.10967 13.1892i 0.317954 0.589838i
\(501\) 3.86639 + 6.69679i 0.172738 + 0.299191i
\(502\) 0.552351 0.358701i 0.0246527 0.0160096i
\(503\) 5.89077 + 9.80389i 0.262657 + 0.437134i 0.960161 0.279446i \(-0.0901509\pi\)
−0.697505 + 0.716580i \(0.745706\pi\)
\(504\) −6.57337 + 26.3644i −0.292801 + 1.17436i
\(505\) 5.57565 + 20.4874i 0.248113 + 0.911679i
\(506\) 13.3646 + 1.40468i 0.594129 + 0.0624454i
\(507\) 12.6574 5.90222i 0.562133 0.262127i
\(508\) −15.7545 0.274996i −0.698993 0.0122010i
\(509\) 8.53761 + 1.19988i 0.378423 + 0.0531839i 0.325821 0.945432i \(-0.394359\pi\)
0.0526025 + 0.998616i \(0.483248\pi\)
\(510\) −5.93932 7.54094i −0.262998 0.333919i
\(511\) 12.9022 31.9341i 0.570759 1.41268i
\(512\) 2.43059 + 4.77030i 0.107418 + 0.210819i
\(513\) 6.23723 + 4.82390i 0.275380 + 0.212980i
\(514\) −20.6925 + 6.72340i −0.912707 + 0.296556i
\(515\) −39.8870 2.63228i −1.75763 0.115992i
\(516\) 19.1157 0.667535i 0.841522 0.0293866i
\(517\) −3.75552 + 1.29313i −0.165167 + 0.0568717i
\(518\) 4.63450 + 6.61875i 0.203628 + 0.290811i
\(519\) 0.0884110 0.0596340i 0.00388081 0.00261764i
\(520\) −6.05660 15.5952i −0.265600 0.683895i
\(521\) −32.7369 + 3.44078i −1.43423 + 0.150743i −0.789538 0.613701i \(-0.789680\pi\)
−0.644690 + 0.764445i \(0.723013\pi\)
\(522\) 15.9018 9.55476i 0.696002 0.418200i
\(523\) 3.40896 + 14.7658i 0.149063 + 0.645665i 0.993866 + 0.110587i \(0.0352732\pi\)
−0.844803 + 0.535078i \(0.820282\pi\)
\(524\) −21.1748 12.2253i −0.925025 0.534064i
\(525\) −32.1183 13.9997i −1.40176 0.610995i
\(526\) 5.04376 13.8576i 0.219919 0.604221i
\(527\) −7.29405 + 9.67953i −0.317734 + 0.421647i
\(528\) 0.0578716 + 3.31546i 0.00251854 + 0.144287i
\(529\) −12.2942 8.29256i −0.534532 0.360546i
\(530\) −9.00744 5.36433i −0.391258 0.233012i
\(531\) −12.4460 + 17.1304i −0.540109 + 0.743396i
\(532\) −10.1064 + 12.1652i −0.438167 + 0.527427i
\(533\) 5.41902 0.858289i 0.234724 0.0371766i
\(534\) 2.61631 1.63485i 0.113219 0.0707469i
\(535\) 11.6015 + 31.4906i 0.501575 + 1.36146i
\(536\) −13.8232 + 7.34995i −0.597073 + 0.317469i
\(537\) 12.9035 + 42.2055i 0.556828 + 1.82130i
\(538\) 2.50807 + 20.4266i 0.108130 + 0.880652i
\(539\) −0.659580 0.593889i −0.0284101 0.0255806i
\(540\) 4.94349 2.22421i 0.212734 0.0957149i
\(541\) −4.36051 10.7926i −0.187473 0.464012i 0.803951 0.594695i \(-0.202727\pi\)
−0.991424 + 0.130684i \(0.958283\pi\)
\(542\) −4.60673 + 5.29944i −0.197876 + 0.227630i
\(543\) 7.42071 + 27.6945i 0.318453 + 1.18848i
\(544\) −1.24075 + 11.8049i −0.0531966 + 0.506132i
\(545\) 0.388006 + 3.06093i 0.0166203 + 0.131116i
\(546\) −14.1078 + 6.88082i −0.603757 + 0.294472i
\(547\) −0.931764 + 0.0162640i −0.0398393 + 0.000695398i −0.0373686 0.999302i \(-0.511898\pi\)
−0.00247072 + 0.999997i \(0.500786\pi\)
\(548\) 21.6999 + 2.66441i 0.926973 + 0.113818i
\(549\) 5.07321 6.04601i 0.216519 0.258038i
\(550\) 10.8029 + 1.62440i 0.460638 + 0.0692648i
\(551\) 26.7987 2.47730i 1.14166 0.105537i
\(552\) −19.6088 + 38.4845i −0.834608 + 1.63801i
\(553\) −21.9465 25.2465i −0.933258 1.07359i
\(554\) −8.69870 + 12.8964i −0.369572 + 0.547914i
\(555\) 6.13706 20.3582i 0.260504 0.864156i
\(556\) −8.74755 + 8.44741i −0.370979 + 0.358250i
\(557\) 8.87732 + 19.0375i 0.376144 + 0.806644i 0.999691 + 0.0248578i \(0.00791328\pi\)
−0.623547 + 0.781786i \(0.714309\pi\)
\(558\) 11.2241 + 13.8607i 0.475156 + 0.586768i
\(559\) 10.1750 + 11.3004i 0.430355 + 0.477957i
\(560\) 1.09069 + 2.66941i 0.0460899 + 0.112803i
\(561\) −7.53244 + 12.0544i −0.318020 + 0.508939i
\(562\) 0.398475 7.60335i 0.0168086 0.320728i
\(563\) 12.1793 + 7.90933i 0.513296 + 0.333338i 0.775159 0.631767i \(-0.217670\pi\)
−0.261862 + 0.965105i \(0.584337\pi\)
\(564\) 0.178760 5.11902i 0.00752716 0.215550i
\(565\) −30.0888 15.8477i −1.26585 0.666719i
\(566\) −1.64019 + 11.6706i −0.0689423 + 0.490550i
\(567\) 8.41986 + 15.1898i 0.353601 + 0.637913i
\(568\) −18.7620 + 1.64146i −0.787237 + 0.0688743i
\(569\) −19.2830 14.0099i −0.808383 0.587325i 0.104978 0.994475i \(-0.466523\pi\)
−0.913361 + 0.407150i \(0.866523\pi\)
\(570\) −20.4851 0.534345i −0.858025 0.0223813i
\(571\) −29.4219 + 21.3762i −1.23127 + 0.894568i −0.996984 0.0776011i \(-0.975274\pi\)
−0.234282 + 0.972169i \(0.575274\pi\)
\(572\) −7.50176 + 6.52118i −0.313664 + 0.272664i
\(573\) 3.94168 32.1024i 0.164666 1.34110i
\(574\) 4.30925 0.759837i 0.179865 0.0317150i
\(575\) −24.7045 18.3146i −1.03025 0.763773i
\(576\) 13.1026 + 4.76896i 0.545942 + 0.198706i
\(577\) 11.9911 0.628427i 0.499196 0.0261618i 0.198923 0.980015i \(-0.436256\pi\)
0.300273 + 0.953853i \(0.402922\pi\)
\(578\) 6.55920 8.09994i 0.272827 0.336913i
\(579\) −45.5744 11.3630i −1.89401 0.472230i
\(580\) 7.16268 17.0596i 0.297414 0.708362i
\(581\) −12.7491 + 5.67628i −0.528924 + 0.235492i
\(582\) −21.7071 5.81641i −0.899790 0.241098i
\(583\) −2.96221 + 15.2393i −0.122682 + 0.631146i
\(584\) −30.4761 16.2044i −1.26111 0.670544i
\(585\) 20.5385 + 9.91792i 0.849161 + 0.410056i
\(586\) 9.31543 + 11.9232i 0.384817 + 0.492543i
\(587\) −34.0443 7.85975i −1.40516 0.324406i −0.546717 0.837317i \(-0.684123\pi\)
−0.858442 + 0.512911i \(0.828567\pi\)
\(588\) 1.01983 0.519629i 0.0420570 0.0214291i
\(589\) 5.94416 + 25.1819i 0.244925 + 1.03760i
\(590\) −0.0407100 10.3977i −0.00167600 0.428068i
\(591\) −13.3822 21.4160i −0.550471 0.880937i
\(592\) −1.53060 + 0.848425i −0.0629072 + 0.0348701i
\(593\) 20.1790 + 14.1295i 0.828651 + 0.580228i 0.909122 0.416529i \(-0.136754\pi\)
−0.0804713 + 0.996757i \(0.525643\pi\)
\(594\) 2.74550 + 2.84305i 0.112649 + 0.116652i
\(595\) −2.31108 + 12.1431i −0.0947449 + 0.497818i
\(596\) −3.40546 1.51621i −0.139493 0.0621062i
\(597\) 54.1939 + 43.8854i 2.21801 + 1.79611i
\(598\) −13.4241 + 3.09919i −0.548950 + 0.126735i
\(599\) 14.4776 12.1482i 0.591541 0.496362i −0.297173 0.954824i \(-0.596044\pi\)
0.888714 + 0.458462i \(0.151599\pi\)
\(600\) −17.3175 + 30.5447i −0.706985 + 1.24698i
\(601\) 34.0766 19.6741i 1.39001 0.802525i 0.396697 0.917949i \(-0.370156\pi\)
0.993316 + 0.115425i \(0.0368229\pi\)
\(602\) 8.27092 + 8.86948i 0.337098 + 0.361493i
\(603\) 6.94869 20.1805i 0.282973 0.821812i
\(604\) 9.26707 + 8.94911i 0.377072 + 0.364134i
\(605\) 1.63893 + 8.25882i 0.0666321 + 0.335769i
\(606\) −4.82966 19.3707i −0.196191 0.786881i
\(607\) −29.8492 + 29.8492i −1.21154 + 1.21154i −0.241024 + 0.970519i \(0.577483\pi\)
−0.970519 + 0.241024i \(0.922517\pi\)
\(608\) 17.6920 + 18.1414i 0.717505 + 0.735730i
\(609\) −41.1477 13.3697i −1.66739 0.541767i
\(610\) −0.255214 + 3.86726i −0.0103333 + 0.156581i
\(611\) 3.20886 2.50703i 0.129816 0.101424i
\(612\) −6.09132 8.08345i −0.246227 0.326754i
\(613\) −38.9621 + 11.9119i −1.57366 + 0.481117i −0.953003 0.302962i \(-0.902025\pi\)
−0.620661 + 0.784079i \(0.713136\pi\)
\(614\) −25.0009 0.873052i −1.00896 0.0352335i
\(615\) −8.58743 7.67149i −0.346279 0.309344i
\(616\) −14.6831 + 13.2207i −0.591598 + 0.532678i
\(617\) 6.56558 + 5.70738i 0.264320 + 0.229770i 0.778082 0.628163i \(-0.216193\pi\)
−0.513761 + 0.857933i \(0.671748\pi\)
\(618\) 37.4419 + 3.27574i 1.50613 + 0.131770i
\(619\) 12.4584 + 27.9820i 0.500746 + 1.12469i 0.970325 + 0.241803i \(0.0777387\pi\)
−0.469580 + 0.882890i \(0.655595\pi\)
\(620\) 17.1997 + 4.53656i 0.690758 + 0.182193i
\(621\) −3.06675 10.6950i −0.123064 0.429176i
\(622\) 21.8888 + 7.53691i 0.877660 + 0.302202i
\(623\) −3.79921 1.16153i −0.152212 0.0465359i
\(624\) −1.16273 3.19459i −0.0465466 0.127886i
\(625\) −19.4004 15.7678i −0.776017 0.630712i
\(626\) 5.09891i 0.203794i
\(627\) 9.51871 + 28.8132i 0.380141 + 1.15069i
\(628\) −2.24151 + 14.1524i −0.0894461 + 0.564741i
\(629\) −7.48340 0.523290i −0.298383 0.0208650i
\(630\) 16.5157 + 7.62280i 0.658000 + 0.303700i
\(631\) 12.7568 26.1553i 0.507841 1.04123i −0.478740 0.877956i \(-0.658907\pi\)
0.986581 0.163271i \(-0.0522046\pi\)
\(632\) −27.4614 + 19.2287i −1.09235 + 0.764875i
\(633\) −60.8774 11.8334i −2.41966 0.470334i
\(634\) 0.367318 + 1.72810i 0.0145881 + 0.0686315i
\(635\) −5.36540 + 25.7373i −0.212919 + 1.02135i
\(636\) −16.9781 10.6091i −0.673227 0.420679i
\(637\) 0.837604 + 0.355542i 0.0331871 + 0.0140871i
\(638\) 13.4715 + 0.706011i 0.533341 + 0.0279512i
\(639\) 17.1804 19.0807i 0.679645 0.754822i
\(640\) 18.3885 5.35083i 0.726871 0.211510i
\(641\) −2.60200 + 4.89365i −0.102773 + 0.193288i −0.929029 0.370007i \(-0.879355\pi\)
0.826256 + 0.563295i \(0.190466\pi\)
\(642\) −10.2730 29.8350i −0.405444 1.17749i
\(643\) 5.51459 11.8261i 0.217474 0.466375i −0.767058 0.641578i \(-0.778280\pi\)
0.984532 + 0.175202i \(0.0560580\pi\)
\(644\) 21.6534 5.39880i 0.853263 0.212742i
\(645\) 4.86904 31.5407i 0.191718 1.24191i
\(646\) 1.41433 + 7.08995i 0.0556460 + 0.278951i
\(647\) −17.0463 2.69986i −0.670158 0.106143i −0.187922 0.982184i \(-0.560175\pi\)
−0.482236 + 0.876041i \(0.660175\pi\)
\(648\) 16.0212 6.80061i 0.629374 0.267153i
\(649\) −14.4686 + 5.26614i −0.567942 + 0.206714i
\(650\) −11.0142 + 2.03115i −0.432012 + 0.0796683i
\(651\) 7.22287 40.9630i 0.283087 1.60546i
\(652\) −22.1206 + 20.6278i −0.866308 + 0.807845i
\(653\) 20.2721 7.78172i 0.793307 0.304522i 0.0722401 0.997387i \(-0.476985\pi\)
0.721067 + 0.692865i \(0.243652\pi\)
\(654\) −0.303241 2.88514i −0.0118576 0.112818i
\(655\) −26.6439 + 30.8938i −1.04106 + 1.20712i
\(656\) 0.0661097 + 0.945413i 0.00258115 + 0.0369122i
\(657\) 45.4521 12.1789i 1.77326 0.475143i
\(658\) 2.52389 2.04380i 0.0983913 0.0796757i
\(659\) 4.16291 5.32828i 0.162164 0.207560i −0.700065 0.714079i \(-0.746846\pi\)
0.862229 + 0.506519i \(0.169068\pi\)
\(660\) 20.5587 + 3.54211i 0.800245 + 0.137876i
\(661\) −1.17648 2.21264i −0.0457598 0.0860617i 0.859019 0.511945i \(-0.171075\pi\)
−0.904778 + 0.425883i \(0.859964\pi\)
\(662\) −0.825038 + 0.884745i −0.0320660 + 0.0343866i
\(663\) 3.27818 14.1994i 0.127314 0.551457i
\(664\) 4.32185 + 13.3013i 0.167720 + 0.516190i
\(665\) 16.7872 + 20.3602i 0.650978 + 0.789537i
\(666\) −3.41127 + 10.4988i −0.132184 + 0.406821i
\(667\) −32.5512 19.5587i −1.26039 0.757316i
\(668\) −3.62881 1.69214i −0.140403 0.0654710i
\(669\) −62.5458 30.5056i −2.41816 1.17942i
\(670\) 3.10350 + 10.0107i 0.119899 + 0.386749i
\(671\) 5.51681 1.58192i 0.212974 0.0610693i
\(672\) −14.5986 38.0308i −0.563155 1.46707i
\(673\) −13.8340 21.3025i −0.533261 0.821150i 0.464667 0.885485i \(-0.346174\pi\)
−0.997928 + 0.0643353i \(0.979507\pi\)
\(674\) −11.2481 13.4050i −0.433262 0.516342i
\(675\) −2.10356 8.79668i −0.0809661 0.338585i
\(676\) −3.61568 + 6.26255i −0.139065 + 0.240867i
\(677\) 0.269492 + 5.14222i 0.0103574 + 0.197632i 0.998907 + 0.0467367i \(0.0148822\pi\)
−0.988550 + 0.150895i \(0.951785\pi\)
\(678\) 27.9658 + 15.5017i 1.07402 + 0.595340i
\(679\) 12.6861 + 26.0104i 0.486849 + 0.998188i
\(680\) 11.8605 + 3.57541i 0.454831 + 0.137111i
\(681\) 20.4914 + 5.87582i 0.785233 + 0.225162i
\(682\) 1.13034 + 12.9198i 0.0432829 + 0.494725i
\(683\) −5.43273 34.3009i −0.207878 1.31249i −0.842093 0.539332i \(-0.818677\pi\)
0.634216 0.773156i \(-0.281323\pi\)
\(684\) −21.5832 1.02483i −0.825256 0.0391855i
\(685\) 11.1366 34.7370i 0.425506 1.32723i
\(686\) −13.6008 5.49509i −0.519282 0.209804i
\(687\) −30.3710 28.3214i −1.15873 1.08053i
\(688\) −2.09773 + 1.58075i −0.0799753 + 0.0602657i
\(689\) −2.21509 15.7612i −0.0843882 0.600453i
\(690\) 22.8549 + 17.7125i 0.870070 + 0.674304i
\(691\) −1.31444 + 0.279393i −0.0500037 + 0.0106286i −0.232846 0.972514i \(-0.574804\pi\)
0.182842 + 0.983142i \(0.441470\pi\)
\(692\) −0.0197886 + 0.0515509i −0.000752248 + 0.00195967i
\(693\) 2.34761 26.8333i 0.0891784 1.01931i
\(694\) −9.87938 + 0.690834i −0.375016 + 0.0262237i
\(695\) 11.1173 + 16.9732i 0.421702 + 0.643832i
\(696\) −17.6355 + 39.6100i −0.668473 + 1.50141i
\(697\) −1.96956 + 3.55317i −0.0746022 + 0.134586i
\(698\) −12.9281 9.74200i −0.489335 0.368740i
\(699\) 8.82040 + 50.0230i 0.333618 + 1.89204i
\(700\) 17.7807 3.60093i 0.672046 0.136102i
\(701\) −15.0557 12.6332i −0.568645 0.477150i 0.312551 0.949901i \(-0.398817\pi\)
−0.881196 + 0.472751i \(0.843261\pi\)
\(702\) −3.61035 1.83957i −0.136264 0.0694299i
\(703\) −11.0679 + 11.5744i −0.417435 + 0.436538i
\(704\) 5.95966 + 8.20276i 0.224613 + 0.309153i
\(705\) −8.33479 1.88990i −0.313906 0.0711776i
\(706\) −2.47272 + 8.62341i −0.0930622 + 0.324546i
\(707\) −14.7455 + 21.0588i −0.554563 + 0.791998i
\(708\) 0.346536 19.8530i 0.0130236 0.746122i
\(709\) 20.6418 + 16.1272i 0.775220 + 0.605668i 0.923642 0.383256i \(-0.125197\pi\)
−0.148422 + 0.988924i \(0.547419\pi\)
\(710\) −1.26881 + 12.5442i −0.0476177 + 0.470776i
\(711\) 9.50217 44.7042i 0.356359 1.67654i
\(712\) −1.55565 + 3.66487i −0.0583003 + 0.137347i
\(713\) 14.2653 33.6068i 0.534238 1.25859i
\(714\) 2.41642 11.3684i 0.0904323 0.425451i
\(715\) 8.34863 + 14.3304i 0.312221 + 0.535926i
\(716\) −18.0077 14.0692i −0.672979 0.525789i
\(717\) −0.924357 + 52.9564i −0.0345207 + 1.97769i
\(718\) −10.5815 + 15.1119i −0.394898 + 0.563973i
\(719\) 7.06878 24.6518i 0.263621 0.919356i −0.712417 0.701756i \(-0.752400\pi\)
0.976038 0.217599i \(-0.0698227\pi\)
\(720\) −2.01585 + 3.38489i −0.0751264 + 0.126148i
\(721\) −28.4486 39.1561i −1.05948 1.45825i
\(722\) 13.5716 + 7.34950i 0.505084 + 0.273520i
\(723\) 33.5904 + 17.1152i 1.24924 + 0.636520i
\(724\) −11.3725 9.54266i −0.422656 0.354650i
\(725\) −25.7279 17.0621i −0.955510 0.633670i
\(726\) −1.37472 7.79641i −0.0510206 0.289352i
\(727\) −0.895858 0.675077i −0.0332255 0.0250372i 0.585072 0.810981i \(-0.301066\pi\)
−0.618298 + 0.785944i \(0.712177\pi\)
\(728\) 9.82050 17.7167i 0.363972 0.656623i
\(729\) −15.3639 + 34.5079i −0.569033 + 1.27807i
\(730\) −14.4713 + 18.0143i −0.535605 + 0.666738i
\(731\) −11.2320 + 0.785420i −0.415431 + 0.0290498i
\(732\) −0.645052 + 7.37297i −0.0238418 + 0.272513i
\(733\) −5.27293 + 13.7365i −0.194760 + 0.507368i −0.995833 0.0911997i \(-0.970930\pi\)
0.801072 + 0.598567i \(0.204263\pi\)
\(734\) −12.8169 + 2.72432i −0.473081 + 0.100557i
\(735\) −0.533582 1.83369i −0.0196815 0.0676368i
\(736\) −4.97623 35.4077i −0.183426 1.30515i
\(737\) 12.3948 9.34018i 0.456570 0.344050i
\(738\) 4.37220 + 4.07714i 0.160943 + 0.150082i
\(739\) 36.9800 + 14.9409i 1.36033 + 0.549610i 0.934749 0.355309i \(-0.115624\pi\)
0.425584 + 0.904919i \(0.360069\pi\)
\(740\) 3.44318 + 10.4575i 0.126574 + 0.384426i
\(741\) −18.8444 24.7534i −0.692266 0.909339i
\(742\) −1.98572 12.5373i −0.0728980 0.460260i
\(743\) 0.642346 + 7.34205i 0.0235654 + 0.269354i 0.998832 + 0.0483211i \(0.0153871\pi\)
−0.975266 + 0.221032i \(0.929057\pi\)
\(744\) −40.0698 11.4898i −1.46903 0.421238i
\(745\) −3.54754 + 5.10887i −0.129972 + 0.187175i
\(746\) 5.95576 + 12.2111i 0.218056 + 0.447081i
\(747\) −16.6760 9.24367i −0.610144 0.338208i
\(748\) −0.385194 7.34994i −0.0140841 0.268740i
\(749\) −20.3168 + 35.1896i −0.742358 + 1.28580i
\(750\) 17.9201 + 15.2119i 0.654349 + 0.555459i
\(751\) 10.5448 + 12.5668i 0.384786 + 0.458571i 0.923319 0.384034i \(-0.125466\pi\)
−0.538532 + 0.842605i \(0.681021\pi\)
\(752\) 0.383095 + 0.589915i 0.0139700 + 0.0215120i
\(753\) −0.752029 1.95910i −0.0274054 0.0713936i
\(754\) −13.2945 + 3.81213i −0.484157 + 0.138830i
\(755\) 17.5593 12.3979i 0.639049 0.451206i
\(756\) 5.89917 + 2.87722i 0.214551 + 0.104643i
\(757\) 2.59366 + 1.20944i 0.0942682 + 0.0439580i 0.469180 0.883102i \(-0.344549\pi\)
−0.374912 + 0.927060i \(0.622327\pi\)
\(758\) −15.5559 9.34694i −0.565017 0.339496i
\(759\) 13.2314 40.7220i 0.480268 1.47811i
\(760\) 22.0509 14.5984i 0.799871 0.529540i
\(761\) 7.53453 + 23.1889i 0.273127 + 0.840597i 0.989709 + 0.143095i \(0.0457054\pi\)
−0.716582 + 0.697502i \(0.754295\pi\)
\(762\) 5.56067 24.0859i 0.201442 0.872540i
\(763\) −2.54779 + 2.73218i −0.0922364 + 0.0989114i
\(764\) 7.86229 + 14.7868i 0.284448 + 0.534968i
\(765\) −15.1497 + 7.46258i −0.547740 + 0.269810i
\(766\) 14.0570 17.9921i 0.507899 0.650082i
\(767\) 12.2677 9.93415i 0.442959 0.358702i
\(768\) −36.2415 + 9.71089i −1.30775 + 0.350412i
\(769\) 2.49856 + 35.7311i 0.0901005 + 1.28850i 0.806679 + 0.590990i \(0.201263\pi\)
−0.716578 + 0.697506i \(0.754293\pi\)
\(770\) 6.85676 + 11.3110i 0.247101 + 0.407621i
\(771\) 7.24640 + 68.9449i 0.260973 + 2.48299i
\(772\) 22.7050 8.71564i 0.817172 0.313683i
\(773\) −26.7615 + 24.9555i −0.962543 + 0.897586i −0.994795 0.101894i \(-0.967510\pi\)
0.0322521 + 0.999480i \(0.489732\pi\)
\(774\) −2.87715 + 16.3172i −0.103417 + 0.586508i
\(775\) 12.8013 26.7768i 0.459838 0.961851i
\(776\) 27.2527 9.91916i 0.978314 0.356077i
\(777\) 23.6984 10.0594i 0.850175 0.360878i
\(778\) 12.7219 + 2.01494i 0.456101 + 0.0722392i
\(779\) 3.14776 + 8.08130i 0.112780 + 0.289543i
\(780\) −21.1112 + 3.42847i −0.755902 + 0.122759i
\(781\) 18.1158 4.51677i 0.648233 0.161623i
\(782\) 4.31126 9.24552i 0.154170 0.330619i
\(783\) −3.63623 10.5604i −0.129948 0.377397i
\(784\) −0.0737907 + 0.138780i −0.00263538 + 0.00495644i
\(785\) 22.4978 + 8.08892i 0.802981 + 0.288706i
\(786\) 25.6666 28.5056i 0.915496 1.01676i
\(787\) −1.98168 0.103855i −0.0706392 0.00370204i 0.0169836 0.999856i \(-0.494594\pi\)
−0.0876228 + 0.996154i \(0.527927\pi\)
\(788\) 12.0364 + 5.10916i 0.428780 + 0.182006i
\(789\) −39.8478 24.8997i −1.41862 0.886452i
\(790\) 9.20849 + 20.4666i 0.327623 + 0.728168i
\(791\) −8.56083 40.2755i −0.304388 1.43203i
\(792\) −26.4980 5.15069i −0.941565 0.183022i
\(793\) −4.81980 + 3.37486i −0.171156 + 0.119845i
\(794\) 3.03695 6.22666i 0.107777 0.220976i
\(795\) −22.6857 + 24.5192i −0.804579 + 0.869607i
\(796\) −36.0198 2.51875i −1.27669 0.0892748i
\(797\) 3.70182 23.3724i 0.131125 0.827891i −0.831197 0.555978i \(-0.812344\pi\)
0.962322 0.271913i \(-0.0876563\pi\)
\(798\) −15.3713 19.4764i −0.544138 0.689456i
\(799\) 3.01518i 0.106670i
\(800\) −2.76002 28.9356i −0.0975813 1.02303i
\(801\) −1.85640 5.10041i −0.0655926 0.180214i
\(802\) −19.6745 6.01508i −0.694729 0.212400i
\(803\) 32.3528 + 11.1400i 1.14171 + 0.393121i
\(804\) 5.51674 + 19.2392i 0.194560 + 0.678513i
\(805\) −2.09430 37.1761i −0.0738144 1.31029i
\(806\) −5.40809 12.1468i −0.190492 0.427852i
\(807\) 65.3236 + 5.71507i 2.29950 + 0.201180i
\(808\) 19.4440 + 16.9024i 0.684037 + 0.594624i
\(809\) 9.32020 8.39195i 0.327681 0.295045i −0.488826 0.872382i \(-0.662575\pi\)
0.816506 + 0.577336i \(0.195908\pi\)
\(810\) −2.46712 11.3875i −0.0866859 0.400115i
\(811\) 13.8368 + 0.483192i 0.485876 + 0.0169672i 0.276791 0.960930i \(-0.410729\pi\)
0.209086 + 0.977897i \(0.432951\pi\)
\(812\) 21.4234 6.54979i 0.751814 0.229852i
\(813\) 13.4646 + 17.8681i 0.472225 + 0.626663i
\(814\) −6.32553 + 4.94205i −0.221710 + 0.173219i
\(815\) 26.9102 + 42.6925i 0.942625 + 1.49545i
\(816\) 2.39404 + 0.777870i 0.0838081 + 0.0272309i
\(817\) −14.0327 + 19.5153i −0.490943 + 0.682753i
\(818\) 9.66725 9.66725i 0.338007 0.338007i
\(819\) 6.68073 + 26.7949i 0.233444 + 0.936291i
\(820\) 5.92071 + 0.703452i 0.206760 + 0.0245656i
\(821\) −13.7461 13.2745i −0.479742 0.463282i 0.415028 0.909809i \(-0.363772\pi\)
−0.894770 + 0.446527i \(0.852661\pi\)
\(822\) −11.1665 + 32.4299i −0.389476 + 1.13112i
\(823\) −18.2230 19.5418i −0.635215 0.681185i 0.329598 0.944121i \(-0.393087\pi\)
−0.964813 + 0.262937i \(0.915309\pi\)
\(824\) −42.0057 + 24.2520i −1.46334 + 0.844859i
\(825\) 12.2192 32.5926i 0.425417 1.13473i
\(826\) 9.64411 8.09237i 0.335561 0.281569i
\(827\) 15.1862 3.50601i 0.528075 0.121916i 0.0475034 0.998871i \(-0.484874\pi\)
0.480572 + 0.876955i \(0.340429\pi\)
\(828\) 23.6945 + 19.1874i 0.823440 + 0.666808i
\(829\) 3.79539 + 1.68982i 0.131819 + 0.0586897i 0.471586 0.881820i \(-0.343682\pi\)
−0.339767 + 0.940510i \(0.610348\pi\)
\(830\) 9.28847 1.17741i 0.322407 0.0408686i
\(831\) 34.4306 + 35.6540i 1.19439 + 1.23682i
\(832\) −8.51502 5.96228i −0.295205 0.206705i
\(833\) −0.589288 + 0.326648i −0.0204176 + 0.0113177i
\(834\) −10.1095 16.1786i −0.350064 0.560219i
\(835\) −3.90560 + 5.42010i −0.135159 + 0.187570i
\(836\) −12.5946 9.39407i −0.435594 0.324901i
\(837\) 9.56734 4.87480i 0.330696 0.168498i
\(838\) 19.2123 + 4.43550i 0.663677 + 0.153222i
\(839\) −2.04474 2.61715i −0.0705924 0.0903541i 0.751418 0.659826i \(-0.229370\pi\)
−0.822011 + 0.569472i \(0.807148\pi\)
\(840\) −41.8383 + 7.54625i −1.44356 + 0.260370i
\(841\) −8.05387 4.28232i −0.277720 0.147666i
\(842\) −0.155653 + 0.800764i −0.00536415 + 0.0275961i
\(843\) −23.4329 6.27882i −0.807071 0.216254i
\(844\) 29.3354 13.0610i 1.00977 0.449577i
\(845\) 9.13697 + 7.88006i 0.314321 + 0.271082i
\(846\) 4.30520 + 1.07341i 0.148016 + 0.0369045i
\(847\) −6.41569 + 7.92272i −0.220446 + 0.272228i
\(848\) 2.74549 0.143885i 0.0942806 0.00494104i
\(849\) 35.2863 + 12.8431i 1.21102 + 0.440776i
\(850\) 3.83586 7.35252i 0.131569 0.252189i
\(851\) 22.2539 3.92396i 0.762853 0.134512i
\(852\) −2.93426 + 23.8977i −0.100526 + 0.818721i
\(853\) −2.56345 + 2.22837i −0.0877708 + 0.0762979i −0.698834 0.715284i \(-0.746298\pi\)
0.611064 + 0.791582i \(0.290742\pi\)
\(854\) −3.79639 + 2.75824i −0.129910 + 0.0943851i
\(855\) −8.41275 + 35.0572i −0.287710 + 1.19893i
\(856\) 32.9441 + 23.9353i 1.12601 + 0.818092i
\(857\) −21.6405 + 1.89330i −0.739225 + 0.0646738i −0.450547 0.892752i \(-0.648771\pi\)
−0.288678 + 0.957426i \(0.593216\pi\)
\(858\) −7.56002 13.6386i −0.258095 0.465615i
\(859\) −4.73808 + 33.7132i −0.161661 + 1.15028i 0.725299 + 0.688434i \(0.241701\pi\)
−0.886960 + 0.461846i \(0.847187\pi\)
\(860\) 7.30212 + 14.8240i 0.249000 + 0.505493i
\(861\) 0.486576 13.9337i 0.0165825 0.474859i
\(862\) 25.2808 + 16.4175i 0.861068 + 0.559184i
\(863\) −1.29626 + 24.7342i −0.0441253 + 0.841961i 0.883496 + 0.468439i \(0.155183\pi\)
−0.927621 + 0.373522i \(0.878150\pi\)
\(864\) 5.57268 8.91814i 0.189586 0.303401i
\(865\) 0.0783237 + 0.0485167i 0.00266309 + 0.00164962i
\(866\) −5.59035 6.20871i −0.189968 0.210981i
\(867\) −20.8993 25.8085i −0.709778 0.876503i
\(868\) 9.10209 + 19.5195i 0.308945 + 0.662535i
\(869\) 23.9061 23.0859i 0.810959 0.783134i
\(870\) 23.8421 + 16.5557i 0.808321 + 0.561289i
\(871\) −8.89759 + 13.1912i −0.301483 + 0.446967i
\(872\) 2.45618 + 2.82551i 0.0831768 + 0.0956839i
\(873\) −17.9497 + 35.2282i −0.607504 + 1.19229i
\(874\) −9.30053 19.6919i −0.314595 0.666089i
\(875\) −0.355531 30.2675i −0.0120192 1.02323i
\(876\) −28.3636 + 33.8024i −0.958317 + 1.14208i
\(877\) −15.9085 1.95332i −0.537192 0.0659589i −0.151274 0.988492i \(-0.548337\pi\)
−0.385918 + 0.922533i \(0.626115\pi\)
\(878\) 24.3070 0.424280i 0.820322 0.0143188i
\(879\) 43.3313 21.1341i 1.46153 0.712836i
\(880\) −2.59162 + 1.22087i −0.0873636 + 0.0411555i
\(881\) 2.39392 22.7767i 0.0806533 0.767365i −0.877204 0.480119i \(-0.840594\pi\)
0.957857 0.287246i \(-0.0927398\pi\)
\(882\) 0.256614 + 0.957697i 0.00864065 + 0.0322473i
\(883\) 26.4577 30.4360i 0.890371 1.02425i −0.109172 0.994023i \(-0.534820\pi\)
0.999543 0.0302317i \(-0.00962450\pi\)
\(884\) 2.82666 + 6.99622i 0.0950708 + 0.235308i
\(885\) −32.4329 6.76120i −1.09022 0.227275i
\(886\) −19.1118 17.2083i −0.642072 0.578124i
\(887\) 1.75400 + 14.2852i 0.0588934 + 0.479648i 0.992583 + 0.121566i \(0.0387916\pi\)
−0.933690 + 0.358083i \(0.883431\pi\)
\(888\) −7.54335 24.6732i −0.253138 0.827978i
\(889\) −28.1062 + 14.9443i −0.942652 + 0.501217i
\(890\) 2.21548 + 1.48177i 0.0742630 + 0.0496691i
\(891\) −14.6321 + 9.14317i −0.490195 + 0.306308i
\(892\) 35.5886 5.63668i 1.19159 0.188730i
\(893\) 4.95116 + 4.11323i 0.165684 + 0.137644i
\(894\) 3.43741 4.73119i 0.114964 0.158235i
\(895\) −28.6782 + 25.1274i −0.958607 + 0.839916i
\(896\) 19.2237 + 12.9666i 0.642220 + 0.433183i
\(897\) 0.766119 + 43.8909i 0.0255800 + 1.46548i
\(898\) −9.83923 + 13.0571i −0.328339 + 0.435721i
\(899\) 12.5350 34.4395i 0.418065 1.14862i
\(900\) 18.5486 + 16.4400i 0.618286 + 0.548001i
\(901\) 10.2062 + 5.89253i 0.340017 + 0.196309i
\(902\) 0.977894 + 4.23572i 0.0325603 + 0.141034i
\(903\) 33.1220 19.9017i 1.10223 0.662288i
\(904\) −41.0381 + 4.31328i −1.36491 + 0.143458i
\(905\) −19.1890 + 15.6637i −0.637864 + 0.520680i
\(906\) −16.7552 + 11.3016i −0.556656 + 0.375469i
\(907\) −3.15459 4.50522i −0.104746 0.149593i 0.763357 0.645977i \(-0.223550\pi\)
−0.868103 + 0.496384i \(0.834661\pi\)
\(908\) −10.4365 + 3.59356i −0.346346 + 0.119257i
\(909\) −35.1016 + 1.22578i −1.16425 + 0.0406564i
\(910\) −10.4221 8.67589i −0.345490 0.287603i
\(911\) −23.9027 + 7.76646i −0.791932 + 0.257314i −0.676927 0.736050i \(-0.736689\pi\)
−0.115006 + 0.993365i \(0.536689\pi\)
\(912\) 4.54320 2.87004i 0.150440 0.0950365i
\(913\) −6.29435 12.3534i −0.208313 0.408837i
\(914\) −3.80349 + 9.41397i −0.125808 + 0.311386i
\(915\) 11.8838 + 3.35732i 0.392865 + 0.110989i
\(916\) 21.2930 + 2.99254i 0.703541 + 0.0988763i
\(917\) −49.3877 0.862066i −1.63093 0.0284679i
\(918\) 2.71919 1.26798i 0.0897468 0.0418496i
\(919\) −11.6570 1.22520i −0.384530 0.0404158i −0.0897086 0.995968i \(-0.528594\pi\)
−0.294822 + 0.955552i \(0.595260\pi\)
\(920\) −37.2716 1.80702i −1.22881 0.0595758i
\(921\) −19.2831 + 77.3404i −0.635401 + 2.54845i
\(922\) −17.3937 28.9479i −0.572829 0.953348i
\(923\) −16.0532 + 10.4251i −0.528399 + 0.343146i
\(924\) 12.6294 + 21.8748i 0.415477 + 0.719628i
\(925\) 18.2150 2.38144i 0.598905 0.0783014i
\(926\) 13.5373 + 2.38699i 0.444863 + 0.0784413i
\(927\) 19.3330 63.2355i 0.634980 2.07692i
\(928\) −6.84879 35.2340i −0.224823 1.15661i
\(929\) 2.75001 39.3270i 0.0902249 1.29028i −0.715763 0.698343i \(-0.753921\pi\)
0.805988 0.591932i \(-0.201635\pi\)
\(930\) −12.5715 + 24.9137i −0.412236 + 0.816951i
\(931\) −0.267512 + 1.41326i −0.00876734 + 0.0463177i
\(932\) −18.5976 18.5976i −0.609183 0.609183i
\(933\) 37.9902 63.2263i 1.24374 2.06994i
\(934\) −1.16504 33.3623i −0.0381212 1.09165i
\(935\) −12.1674 1.66146i −0.397916 0.0543356i
\(936\) 27.4055 3.85159i 0.895777 0.125893i
\(937\) −34.9258 + 4.28835i −1.14098 + 0.140094i −0.670216 0.742166i \(-0.733798\pi\)
−0.470761 + 0.882261i \(0.656021\pi\)
\(938\) −6.91144 + 10.6427i −0.225667 + 0.347496i
\(939\) 15.8914 + 3.37783i 0.518597 + 0.110231i
\(940\) 4.09647 1.67377i 0.133612 0.0545923i
\(941\) 3.80396 1.53690i 0.124006 0.0501016i −0.311765 0.950159i \(-0.600920\pi\)
0.435771 + 0.900058i \(0.356476\pi\)
\(942\) −20.9860 8.05576i −0.683760 0.262471i
\(943\) 3.16730 11.8205i 0.103142 0.384929i
\(944\) 1.52476 + 2.26054i 0.0496266 + 0.0735745i
\(945\) 6.55629 8.77173i 0.213276 0.285344i
\(946\) −8.36942 + 8.66679i −0.272113 + 0.281782i
\(947\) −46.4833 + 9.03545i −1.51051 + 0.293613i −0.877138 0.480238i \(-0.840550\pi\)
−0.633368 + 0.773851i \(0.718328\pi\)
\(948\) 16.7458 + 39.4506i 0.543877 + 1.28129i
\(949\) −35.0800 −1.13875
\(950\) −6.84061 16.3289i −0.221939 0.529779i
\(951\) 5.62918 0.182539
\(952\) 5.86052 + 13.8065i 0.189941 + 0.447472i
\(953\) −36.0026 + 6.99820i −1.16624 + 0.226694i −0.736614 0.676314i \(-0.763576\pi\)
−0.429625 + 0.903007i \(0.641354\pi\)
\(954\) 12.0470 12.4750i 0.390036 0.403894i
\(955\) 26.6896 8.27424i 0.863657 0.267748i
\(956\) −15.3355 22.7359i −0.495986 0.735330i
\(957\) 11.1247 41.5180i 0.359611 1.34209i
\(958\) −21.1720 8.12717i −0.684037 0.262577i
\(959\) 40.9514 16.5455i 1.32239 0.534281i
\(960\) 1.60704 + 21.7572i 0.0518669 + 0.702211i
\(961\) 4.14231 + 0.880475i 0.133623 + 0.0284024i
\(962\) 4.48221 6.90200i 0.144512 0.222529i
\(963\) −55.1007 + 6.76552i −1.77560 + 0.218016i
\(964\) −19.3304 + 2.71671i −0.622589 + 0.0874992i
\(965\) −7.20286 39.9345i −0.231868 1.28554i
\(966\) 1.22183 + 34.9885i 0.0393116 + 1.12574i
\(967\) −9.27507 + 15.4363i −0.298266 + 0.496398i −0.969580 0.244775i \(-0.921286\pi\)
0.671314 + 0.741173i \(0.265730\pi\)
\(968\) 7.22425 + 7.22425i 0.232196 + 0.232196i
\(969\) 23.0337 + 0.288873i 0.739950 + 0.00927995i
\(970\) −3.11226 19.1641i −0.0999287 0.615323i
\(971\) −0.0364179 + 0.520801i −0.00116871 + 0.0167133i −0.998113 0.0613974i \(-0.980444\pi\)
0.996945 + 0.0781107i \(0.0248888\pi\)
\(972\) −5.63330 28.9808i −0.180688 0.929561i
\(973\) −7.18264 + 23.4934i −0.230265 + 0.753163i
\(974\) −16.4864 2.90700i −0.528258 0.0931462i
\(975\) −0.966114 + 35.6727i −0.0309404 + 1.14244i
\(976\) −0.508176 0.880187i −0.0162663 0.0281741i
\(977\) 19.8355 12.8813i 0.634594 0.412110i −0.186859 0.982387i \(-0.559831\pi\)
0.821453 + 0.570277i \(0.193164\pi\)
\(978\) −24.4386 40.6726i −0.781460 1.30057i
\(979\) 0.954829 3.82961i 0.0305165 0.122395i
\(980\) 0.770909 + 0.619288i 0.0246258 + 0.0197824i
\(981\) −5.07596 0.533505i −0.162063 0.0170335i
\(982\) −1.34599 + 0.627646i −0.0429523 + 0.0200290i
\(983\) −2.09187 0.0365137i −0.0667202 0.00116461i −0.0159174 0.999873i \(-0.505067\pi\)
−0.0508028 + 0.998709i \(0.516178\pi\)
\(984\) −13.8363 1.94457i −0.441085 0.0619905i
\(985\) 12.1292 18.1350i 0.386468 0.577829i
\(986\) 3.83620 9.49492i 0.122169 0.302380i
\(987\) −4.69780 9.21996i −0.149533 0.293475i
\(988\) 15.3444 + 4.90248i 0.488169 + 0.155969i
\(989\) 32.2567 10.4808i 1.02570 0.333271i
\(990\) −6.70390 + 16.7816i −0.213064 + 0.533355i
\(991\) 30.3297 1.05913i 0.963453 0.0336445i 0.451149 0.892449i \(-0.351014\pi\)
0.512304 + 0.858804i \(0.328792\pi\)
\(992\) 32.6277 11.2346i 1.03593 0.356699i
\(993\) 2.21087 + 3.15745i 0.0701598 + 0.100199i
\(994\) −12.6559 + 8.53654i −0.401422 + 0.270763i
\(995\) −15.3649 + 58.2541i −0.487102 + 1.84678i
\(996\) 17.7816 1.86892i 0.563432 0.0592191i
\(997\) −6.15631 + 3.69908i −0.194972 + 0.117151i −0.609182 0.793030i \(-0.708502\pi\)
0.414210 + 0.910181i \(0.364058\pi\)
\(998\) −6.82977 29.5830i −0.216193 0.936433i
\(999\) 5.75564 + 3.32302i 0.182100 + 0.105136i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 475.2.bi.a.117.18 yes 2304
19.13 odd 18 inner 475.2.bi.a.317.31 yes 2304
25.3 odd 20 inner 475.2.bi.a.3.31 2304
475.203 even 180 inner 475.2.bi.a.203.18 yes 2304
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
475.2.bi.a.3.31 2304 25.3 odd 20 inner
475.2.bi.a.117.18 yes 2304 1.1 even 1 trivial
475.2.bi.a.203.18 yes 2304 475.203 even 180 inner
475.2.bi.a.317.31 yes 2304 19.13 odd 18 inner